Abstract:
The oblateness and the photogravitational effects of both the primaries on the location and the stability of the triangular equilibrium points in the elliptical restricted three-body problem have been discussed. The stability of the triangular points under the photogravitational and oblateness effects of both the primaries around the binary systems Achird, Lyeten, Alpha Cen-AB, Kruger 60, and Xi-Bootis, has been studied using simulation techniques by drawing different curves of zero velocity. 1. Introduction The present paper is devoted to the analysis of the photogravitational and the oblateness effects of both primaries on the stability of triangular equilibrium points of the planar elliptical restricted three-body problem. The elliptical restricted three-body problem describes the dynamical system more accurately on account that the realistic assumptions of the motion of the primaries are subjected to move along the elliptical orbit. We have attempted to investigate the stability of triangular equilibrium points under the photogravitational and oblateness effects of both the primaries. The bodies of the elliptical restricted three-body problem are generally considered to be spherical in shape, but in actual situations, we have observed that several heavenly bodies are either oblate spheroid or triaxial rigid bodies. The Earth, Jupiter, and Saturn are examples of the oblate spheroid. The lack of sphericity in heavenly bodies causes large perturbation. In addition to the oblateness of heavenly bodies, the triaxiality, the radiation forces of the bodies, the atmospheric drag, and the solar wind are also causes of perturbation. This motivates studies of stability of triangular equilibrium points under the influence of oblateness and radiation of the primaries in the elliptical restricted three-body problem. The stability of the infinitesimal around the triangular equilibrium points in the elliptical restricted three-body problem described in considerable details is due to [1] and the problem was also studied [2–9]. The stability of motion of infinitesimal around one of the triangular equilibrium points ( ) also depends on and . Nonlinear stability of the triangular equilibrium points of the elliptical restricted three-body problem with or without radiation pressure was studied [10–12]. Furthermore, the nonlinear stability of the infinitesimal in the orbits or the size of the stable region around was studied numerically by [11] and the parametric resonance stability around in the elliptical restricted three-body problem has been studied [10]. The

Abstract:
An efficient way to find the workability limit for powder metallurgy parts has been suggested. Compacts of Al-4%TiC, Al-4%WC, Al-4%Fe3C, and Al-4%Mo2C were produced to the relative density of 0.82 and 0.86 with three different geometries through primary operations of powder metallurgy routes. Each sintered compact was hot deformed to various strain levels till a visible crack appeared at the free surface. Oyane’s fracture principle was used to develop a theory to study powder metallurgy compacts. A least square technique was used to determine the constants in fracture criteria and these equations were finally used to find workability limit. It is found that the projected technique was well in agreement with the experimental values. 1. Introduction Powder metallurgy manufacturing technique is used to produce parts to close tolerance, intricate shapes, and near net shapes. It has proved to be cost effective of producing many parts such as porous materials, composite materials, refractory materials, and special high duty alloys [1–3] to be used in aircraft, automotive, and manufacturing industry. Further, powder metallurgy route is green manufacturing and energy efficient manufacturing compared to casting operation [4]. Aluminum metal matrix is used for wide range of industrial applications due to its exceptional properties such as low specific density, great strength, low thermal growth, and decent wear resistance and is cost-effective [5–9]. Ductile aluminum matrix strengthened with tougher and stiffer carbides offers a blend of properties of the metallic material and ceramic strengthening parts [10]. Titanium carbide and tungsten carbide based parts are presently used in high strength application where better strength, wear resistance, and corrosion resistance are necessary [11, 12] and aluminium reinforced with tungsten carbide prepared by warm accumulative roll bonding method exhibited enhanced mechanical properties [13]. The workability of the powder metallurgy parts plays an important part in defining if the powder metallurgy part will be shaped successfully or fracture initiates in the forming practice. Workability is the amount of deformation in which a material can sustain the induced internal stresses of forming prior to failure. Workability features are dependent not only on the material but also on numerous forming parameters such as stress and strain rate, porosity, friction, and temperature [14, 15]. Over the years, numerous models [16–18] were established to study workability of conventional parts; however, they cannot be directly applied

Abstract:
We show that two commonly used definitions for the heat current give different results--through the Kubo formula--for the heat conductivity of oscillator chains. The difference exists for finite chains, and is expected to be important more generally for small structures. For a chain of N particles that are tethered at the ends, the ratio of the heat conductivities calculated with the two currents differs from unity by O(1/N). For a chain held at constant pressure, the difference from unity decays more slowly, and is consistent with O(1/N^eta) with 1 > eta > 0.5.

Abstract:
We present a simple mass model for the lensing galaxy in the gravitationally lensed quasar 0957+561. The model is a generalization of the singular isothermal sphere and includes a core radius, $r_c$, and a power-law index, $\eta$, defined such that mass increases as $r^\eta$ at large radius. We approximate the galaxy cluster surrounding the lensing galaxy with a quadratic potential described by its convergence $\kappa$ and shear $\gamma$. We fit the model to a recent high resolution VLBI map of the two images of 0957+561. We obtain a tight constraint on the radial index, $1.07 < \eta <1.18$, which means that the lens galaxy is nearly isothermal with increasing mass-to-light ratio out to $15 h^{-1}$ kpc. We also obtain an upper limit on the core radius, $r_c < 330 h^{-1}$ pc. We use the model to calculate the Hubble constant $H_0$ as a function of the time delay $\Delta\tau_{BA}$ between the two images: $H_0 = \left({ 82.5^{+5.9} _{-3.0} }\right) (1 - \kappa) \left({ \Delta\tau_{BA}/1.1 \,{\rm yr} }\right)^{-1}$ km/s/Mpc. Once $\Delta \tau_{BA}$ is measured, this will provide an upper bound on $H_0$ since $\kappa$ cannot be negative. In addition, the model degeneracy due to $\kappa$ can be eliminated if the one-dimensional velocity dispersion $\sigma$ of the lensing galaxy is measured. We then have $H_0 = \left({ 82.5^{+8.7} _{-5.6} }\right) (\sigma / 322\,{\rm km/s})^2 \left({ \Delta \tau_{BA} /1.1 \,{\rm yr} }\right)^{-1}$ km/s/Mpc. We investigate the effects of ellipticity in the lensing galaxy and clumpiness in the lensing cluster and find that these cause little change in our results.

Abstract:
The critical behavior of charge-density waves (CDWs) in the pinned phase is studied for applied fields increasing toward the threshold field, using recently developed renormalization group techniques and simulations of automaton models. Despite the existence of many metastable states in the pinned state of the CDW, the renormalization group treatment can be used successfully to find the divergences in the polarization and the correlation length, and, to first order in an $\epsilon = 4-d$ expansion, the diverging time scale. The automaton models studied are a charge-density wave model and a ``sandpile'' model with periodic boundary conditions; these models are found to have the same critical behavior, associated with diverging avalanche sizes. The numerical results for the polarization and the diverging length and time scales in dimensions $d=2,3$ are in agreement with the analytical treatment. These results clarify the connections between the behaviour above and below threshold: the characteristic correlation lengths on both sides of the transition diverge with different exponents. The scaling of the distribution of avalanches on the approach to threshold is found to be different for automaton and continuous-variable models.

Abstract:
We propose a scheme for quantizing a scalar field over the Schwarzschild manifold including the interior of the horizon. On the exterior, the timelike Killing vector and on the horizon the isometry corresponding to restricted Lorentz boosts can be used to enforce the spectral condition. For the interior we appeal to the need for CPT invariance to construct an explicitly positive definite operator which allows identification of positive and negative frequencies. This operator is the translation operator corresponding to the inexorable propagation to smaller radii as expected from the classical metric. We also propose an expression for the propagator in the interior and express it as a mode sum.

Abstract:
We give two direct, elementary proofs that a Monte Carlo simulation converges to equilibrium provided that appropriate conditions are satisfied. The first proof requires detailed balance while the second is quite general.

Abstract:
We discuss different free energies for materials in static electric and magnetic fields. We explain what the corresponding Hamiltonians are, and describe which choice gives rise to which result for the free energy change, dF, in the thermodynamic identity. We also discuss which Hamiltonian is the most appropriate for calculations using statistical mechanics, as well as the relationship between the various free energies and the "Landau function", which has to be minimized to determine the equilibrium polarization or magnetization, and is central to Landau's theory of second order phase transitions.

Abstract:
Large test data volume is one of the major problems in the emerging System-on-Chip (SoC) and this can be reduced by test data compression techniques. Variable-to-variable length compression is one among the test data compression techniques. This study demonstrates a variable-to-variable length based compression technique called Run-Length based Efficient Compression. The patterns which are selected for doing compression can be partitioned into blocks having equal width. The partitioned blocks can be compared with the adjacent one and can be merged. A control code is used to denote the number of blocks merged. The proposed method can be tested by calculating the effect of compression on larger ISCAS’89 benchmark circuits.

Various investigators such as Khan ([1-4]), Khan and Ram [5], Chandra [6,7], Leindler [8], Mishra et al. [9], Mishra [10], Mittal et al. [11], Mittal, Rhoades and Mishra [12], Mittal and Mishra [13], Rhoades et al. [14] have determined the degree of approximation of 2π-periodic signals (functions) belonging to various classes Lipα,Lip(α,r), Lip(ξ(t),r)andW(L_{r},ζ(t)) of functions through trigonometric Fourier approximation (TFA) using different